Appendix C Alternative parallel algorithm

It is straightforward to see that equation 2.21 obeys this equation. 

When the calculation of 8ui and buj is computationally expensive and not easy to calculate in parallel, IN-DC-CBMC will fail because too many correction terms have to be calculated and OUT-DC-CBMC will fail because the calculation of buz cannot be parallelized. This might be true for the simulation of polarizable molecules [108], in which an iterative scheme is used to calculated the polarization energy. In this case, the following algorithm Ccin be used [109]  

Among Q processors, g new (n) chains are divided and grown using the standard CBMC algorithm. We also assume that mod (g, Q) =0. For the selection of trial segments, u is used only. This results in a Rosenbluth factor W for each chain. 

On each processor a, one of the g/Q chains that was grown on processor a is chosen with a probability 

This is the main difference from the IN/OUT-DC-CBMC scheme in which one chain is chosen from all chains on all processors. 

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